Finite Group Databasebeta

← #34077082

Subgroups — #34077082

Order 19328.

408 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 137 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752154C212yesmaximal, complemented
2#23752148C211yesmaximal, characteristic
3#23752148C211yesmaximal, characteristic
4#23752145C212yesmaximal, complemented
5#23752109C212yesmaximal, complemented
6#23752108C212yesmaximal, complemented
7#23752105C212yesmaximal
8#23752085C212yesmaximal
9#385×C151C211yesmaximal, characteristic
10C2×C4⋊Dic151C2212yes—
11C2×C4⋊Dic151C2211yescharacteristic
12C2×C4⋊Dic151C2211yescharacteristic
13C2×Dic151⋊C4C2212yes—
14C2×Dic151⋊C4C2212yes—
15C2×Dic151⋊C4C2212yes—
16C2×Dic151⋊C4C2212yes—
17C2×C22⋊Dic151C2212yes—
18C2×C22⋊Dic151C2212yes—
19C2×C4×Dic151C2212yes—
20C151⋊#95C2212yes—
21C151⋊#95C2212yes—
22C151⋊#95C2212yes—
23C151⋊#95C2212yes—
24C151⋊#95C2211yescharacteristic
25C151⋊#95C2211yescharacteristic
26C23×C4×C151C2211yescharacteristic
27C2×C4⋊C4×C151C2212yes—
28C2×C22⋊C4×C151C2211yescharacteristic
29C2×C22⋊C4×C151C2211yescharacteristic
30#95×C151C2212yes—
31C22×Dic151C2312yes—
32C22×Dic151C2312yes—
33C22×Dic151C2312yes—
34C22×Dic151C2312yes—
35C4⋊Dic151—24no—
36C4⋊Dic151—41no—
37C4⋊Dic151—41no—
38Dic151⋊C4—24no—
39Dic151⋊C4—42no—
40Dic151⋊C4—42no—
41Dic151⋊C4—42no—
42C22⋊Dic151—24no—
43C22⋊Dic151—42no—
44C4×Dic151—42no—
45C24×C151C2311yescharacteristic
46C22×C4×C151—41no—
47C22×C4×C151—42no—
48C22×C4×C151C2311yescharacteristic
49C22×C4×C151C2311yescharacteristic
50C22×C4×C151C2312yes—
51C22×C4×C151C2312yes—
52C4⋊C4×C151—42no—
53C22⋊C4×C151—41no—
54C22⋊C4×C151Q814yes—
55C2×Dic151—22no—
56C2×Dic151—22no—
57C2×Dic151—22no—
58C2×Dic151—22no—
59C2×Dic151—22no—
60C2×Dic151—22no—
61C2×Dic151—22no—
62C2×Dic151—22no—
63C2×Dic151—22no—
64C2×Dic151—22no—
65C2×Dic151—22no—
66C2×Dic151#4114yes—
67C23×C151—22no—
68C23×C151—22no—
69C23×C151—21no—
70C23×C151—21no—
71C23×C151C2×Q812yes—
72C23×C151C2411yescharacteristic
73C2×C4×C151—22no—
74C2×C4×C151—22no—
75C2×C4×C151—22no—
76C2×C4×C151—22no—
77C2×C4×C151—22no—
78C2×C4×C151—22no—
79C2×C4×C151—21no—
80C2×C4×C151—21no—
81C2×C4×C151—22no—
82C2×C4×C151—44no—
83C2×C4×C151C2×Q814yes—
84C22×C151—22no—
85C22×C151—24no—
86C22×C151—42no—
87C22×C151—41no—
88C22×C151—41no—
89C22×C151C22×Q811yescharacteristic
90C22×C151C2×#4112yes—
91C22×C151H(5,𝔽2)12yes—
92C22×C151H(5,𝔽2)11yescharacteristic
93C22×C1512−1+411yescharacteristic
94C4×C151—24no—
95C4×C151—41no—
96C4×C151—41no—
97C4×C151—42no—
98Dic151—24no—
99Dic151—42no—
100Dic151—42no—
101Dic151—42no—
102C2×C151—42no—
103C2×C151#53912yes—
104C2×C151#54411yescharacteristic
105C2×C151#55412yes—
106C2×C151#55911yescharacteristic
107C2×C151#56011yescharacteristic
108C151#280711yescharacteristic, complemented, Sylow
109#2807—1511nomaximal, Sylow
110#400—1512no—
111#399—1511no—
112#399—1511no—
113#398—1512no—
114#389—1512no—
115#389—1512no—
116#388—1512no—
117#385—1512no—
118#385D15111yescharacteristic
119C23×C4C2×D15111yescharacteristic
120C2×C4⋊C4—1512no—
121C2×C4⋊C4—1512no—
122C2×C4⋊C4—1512no—
123C2×C4⋊C4—1512no—
124C2×C4⋊C4—1512no—
125C2×C4⋊C4—1511no—
126C2×C4⋊C4—1511no—
127C2×C4⋊C4C2×D15112yes—
128C2×C22⋊C4—1512no—
129C2×C22⋊C4—1512no—
130C2×C22⋊C4C2×D15111yescharacteristic
131C2×C22⋊C4C2×D15111yescharacteristic
132C2×C42—1512no—
133#95—1512no—
134#95—1512no—
135#95—1512no—
136#95—1512no—
137#95—1511no—
138#95—1511no—
139#95C2×D15112yes—
140C24C22×D15111yescharacteristic
141C22×C4—42no—
142C22×C4—41no—
143C22×C4—1512no—
144C22×C4—1512no—
145C22×C4—1512no—
146C22×C4—1512no—
147C22×C4C22×D15112yes—
148C22×C4C22×D15111yescharacteristic
149C22×C4C22×D15111yescharacteristic
150C22×C4C22×D15112yes—
151C4⋊C4—42no—
152C4⋊C4—3024no—
153C4⋊C4—3024no—
154C4⋊C4—6042no—
155C4⋊C4—6042no—
156C4⋊C4—6042no—
157C4⋊C4—6041no—
158C4⋊C4—6041no—
159C22⋊C4—41no—
160C22⋊C4—3024no—
161C22⋊C4—6042no—
162C22⋊C4Dic30214yes—
163C42—6042no—
164C23—22no—
165C23—21no—
166C23—22no—
167C23—21no—
168C23C2×Dic30212yes—
169C23C23×D15111yescharacteristic
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—44no—
180C2×C4—3022no—
181C2×C4—3022no—
182C2×C4—3022no—
183C2×C4—3022no—
184C2×C4—3022no—
185C2×C4—3022no—
186C2×C4—3022no—
187C2×C4—3022no—
188C2×C4—3022no—
189C2×C4—3022no—
190C2×C4—3022no—
191C2×C4—1514no—
192C2×C4C2×Dic30214yes—
193C22—22no—
194C22—24no—
195C22—42no—
196C22—41no—
197C22—41no—
198C22C22×Dic30211yescharacteristic
199C22#41×D15112yes—
200C22#1801278412yes—
201C22#1801278411yescharacteristic
202C22#1801278711yescharacteristic
203C4—24no—
204C4—41no—
205C4—42no—
206C4—41no—
207C4—3024no—
208C4—6042no—
209C4—6042no—
210C4—6042no—
211C2—42no—
212C2#2375280812yes—
213C2#2375284311yescharacteristic
214C2#2375292112yes—
215C2#2375294611yescharacteristic
216C2#2375295111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D151
commutator, socle, cosocleC23×C151C24
Fitting#385×C151C2
prime radicalC24×C151C23
hypercenter#385D151
hypocenterC151#2807
LCSG ▷ C23×C151 ▷ C151
UCSC1 ◁ C23 ◁ #385

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #23752154C2semidirect
4. #23752145C2semidirect
5. #23752109C2semidirect
6. #23752108C2semidirect
108. C151#2807semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237521542
#237521482
#237521452
#237521092
#237521082
#237521052
#237520852
#385×C1512
#2807151